Was Matthias present when Jesus commissioned the 11? No. There is no evidence of anyone other than the 11. So Matthias' lot casting was a human thing, not a God thing.
Ummm...NO.
Acts chapter 1
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15] And in those days Peter stood up in the midst of the disciples, and said, (the number of names together were about an hundred and twenty,)
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16] Men and brethren, this scripture must needs have been fulfilled, which the Holy Ghost by the mouth of David spake before concerning Judas, which was guide to them that took Jesus.
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17] For he was numbered with us, and had obtained part of this ministry.
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18] Now this man purchased a field with the reward of iniquity; and falling headlong, he burst asunder in the midst, and all his bowels gushed out.
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19] And it was known unto all the dwellers at Jerusalem; insomuch as that field is called in their proper tongue, Aceldama, that is to say, The field of blood.
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20] For it is written in the book of Psalms, Let his habitation be desolate, and let no man dwell therein: and his bishoprick let another take.
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21]
Wherefore of these men which have companied with us all the time that the Lord Jesus went in and out among us,
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22]
Beginning from the baptism of John, unto that same day that he was taken up from us, must one be ordained to be a witness with us of his resurrection.
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23] And they appointed two, Joseph called Barsabas, who was surnamed Justus, and Matthias.
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24] And they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen,
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25] That he may take part of this ministry and apostleship, from which Judas by transgression fell, that he might go to his own place.
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26] And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles.
According to Peter, Matthias "companied with us all the time that the Lord Jesus went in and out among us, beginning from the baptism of John, unto that same day that he was taken up from us", so there's the evidence that you claim doesn't exist.
As far as your dismissal of God in relation to Matthias' calling as an apostle is concerned, you couldn't possibly be more wrong.
For starters, God had foretold "in the book of Psalms" (vs . 20), as Peter so rightly noted, that somebody was going to need to take Judas' place or "his bishoprick let another take" (vs. 20).
This is what Peter was referring to:
"Let his days be few; and let another take his office." (Psalm 109:8)
GOD is the one who foreordained Judas' replacement, and GOD is the one to whom those gathered in the upper room prayed:
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24] And they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen,
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25] That he may take part of this ministry and apostleship, from which Judas by transgression fell, that he might go to his own place.
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26] And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles.
With such being the case, who are you to allege that "Matthias' lot casting was a human thing, not a God thing"?
Furthermore, PAUL HIMSELF recognized Matthias as one of the twelve, when he said:
I Corinthians chapter 15
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1] Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand;
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2] By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain.
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3] For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures;
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4] And that he was buried, and that he rose again the third day according to the scriptures:
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5] And that he was seen of Cephas,
then of the twelve:
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6] After that, he was seen of above five hundred brethren at once; of whom the greater part remain unto this present, but some are fallen asleep.
Jesus "was seen of Cephas" or Peter AFTER HIS RESURRECTION FROM THE DEAD, AND AFTER JUDAS HAD DIED, AND "THEN OF THE TWELVE", and "the twelve" included Matthias.
Just for the record.